A simple person's approach to understanding the contagion condition for spreading processes on generalized random networks

Abstract

We present derivations of the contagion condition for a range of spreading mechanisms on families of generalized random networks and bipartite random networks. We show how the contagion condition can be broken into three elements, two structural in nature, and the third a meshing of the contagion process and the network. The contagion conditions we obtain reflect the spreading dynamics in a clear, interpretable way. For threshold contagion, we discuss results for all-to-all and random network versions of the model, and draw connections between them.

arXiv comment10 pages, 9 figures; chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Nature